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Chapter 6: Quadrilaterals - Coggle Diagram
Chapter 6: Quadrilaterals
6.1 : Classifying Quadrilaterals
Types Of Quadrilaterals
Parallelogram
A Quadrilateral With Both Pairs Of Opposite Sides Parallel.
Rhombus
A parallelogram with four congruent sides.
Kite
A Quadrilateral With Two Pairs Of Adjacent Sides Congruent And No Opposite Sides Congruent.
Rectangle
A parallelogram with four right angles.
Square
A Rhombus With 90° Angles
Trapezoid
One pair of parallel sides.
Isosceles trapezoid
A trapezoid where non-parallel opposite sides are congruent.
Regular trapezoid
A quadrilateral whose non-parallel opposite sides are not congruent.
6.3: Proving that a quadrilateral is a parallelogram
Theorems
Theorem 6.5 - if both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Theorem 6.6 - if both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Theorem 6.7 - If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Theorem 6.8 - If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.
6.2: Properties of Parallelograms
Theorems
Theorem 6.2 - Opposite angles of a
parallelogram are congruent
Theorem 6.3 - The diagonals of a
parallelogram bisect each other
Theorem 6.1 - Opposite sides of a
parallelogram are congruent
Theorem 6.4 - If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal
6.4 Special Parallelograms
Theorem 6-11 : The diagonals of a rectangle are congruent
Theorem 6-12 : If the diagonals of a parallelogram bisects two angles of the parallelogram, then the parallelogram is a rhombus
Theorem 6-10 : The diagonals of a rhombus are perpendicular
Theorem 6-13 : If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle
Theorem 6-9 : Each diagonal of a rhombus bisects two angles of the rhombus
6.5 Trapezoids and Kites
Theorems
Theorem 6.15 - The base angles of an isosceles trapezoid are congruent.
Theorem 6.16 - The diagonals of an isosceles trapezoids are congruent.
Theorem 6.17 - The diagonals of a kite are perpindicular.
6.7 : Proofs Using Coordinate Geometry
Trapezoid Midsegment
Trapezoid Midsegment Theorems
The midsegment of a trapezoid is parallel to the bases
The length of the midsegment of a trapezoid is half the sum of the lengths of the bases.
A trapezoid midsegment is the segment that joins the midpoints of the nonparallel opposite sides
6.6: Placing Figures in the Coordinate Plane
Tips
Put a vertex at the origin so it is easier to tell the length.
You could also make the midpoint the origin.
You could use multiples of two to avoid fractions as midpoints.